What is the integral from 3 to infinity of 3/(x^6) ?

The integral from 3 to infinity of 3/(x^6) is 1/405

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integral from 3 to infinity of 3/(x^6)

\int_{3}^{\infty} \frac{3}{x ^{6}} d x

\frac{1}{405}

Decimal

0.00246 \dots

Solution steps

\int_{3}^{\infty} \frac{3}{x ^{6}} d x

Compute the indefinite integral:

\int \frac{3}{x ^{6}} d x = - \frac{3}{5 x ^{5}} + C

Compute the boundaries:

\int_{3}^{\infty} \frac{3}{x ^{6}} d x = 0 - (- \frac{1}{405})

= 0 - (- \frac{1}{405})

Simplify

= \frac{1}{405}

What is the integral from 3 to infinity of 3/(x^6) ?
The integral from 3 to infinity of 3/(x^6) is 1/405